1 //===-- APFloat.cpp - Implement APFloat class -----------------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file implements a class to represent arbitrary precision floating
11 // point values and provide a variety of arithmetic operations on them.
13 //===----------------------------------------------------------------------===//
15 #include "llvm/ADT/APFloat.h"
16 #include "llvm/ADT/FoldingSet.h"
17 #include "llvm/Support/MathExtras.h"
22 #define convolve(lhs, rhs) ((lhs) * 4 + (rhs))
24 /* Assumed in hexadecimal significand parsing, and conversion to
25 hexadecimal strings. */
26 #define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1]
27 COMPILE_TIME_ASSERT(integerPartWidth % 4 == 0);
31 /* Represents floating point arithmetic semantics. */
33 /* The largest E such that 2^E is representable; this matches the
34 definition of IEEE 754. */
35 exponent_t maxExponent;
37 /* The smallest E such that 2^E is a normalized number; this
38 matches the definition of IEEE 754. */
39 exponent_t minExponent;
41 /* Number of bits in the significand. This includes the integer
43 unsigned int precision;
45 /* True if arithmetic is supported. */
46 unsigned int arithmeticOK;
49 const fltSemantics APFloat::IEEEsingle = { 127, -126, 24, true };
50 const fltSemantics APFloat::IEEEdouble = { 1023, -1022, 53, true };
51 const fltSemantics APFloat::IEEEquad = { 16383, -16382, 113, true };
52 const fltSemantics APFloat::x87DoubleExtended = { 16383, -16382, 64, true };
53 const fltSemantics APFloat::Bogus = { 0, 0, 0, true };
55 // The PowerPC format consists of two doubles. It does not map cleanly
56 // onto the usual format above. For now only storage of constants of
57 // this type is supported, no arithmetic.
58 const fltSemantics APFloat::PPCDoubleDouble = { 1023, -1022, 106, false };
60 /* A tight upper bound on number of parts required to hold the value
63 power * 815 / (351 * integerPartWidth) + 1
65 However, whilst the result may require only this many parts,
66 because we are multiplying two values to get it, the
67 multiplication may require an extra part with the excess part
68 being zero (consider the trivial case of 1 * 1, tcFullMultiply
69 requires two parts to hold the single-part result). So we add an
70 extra one to guarantee enough space whilst multiplying. */
71 const unsigned int maxExponent = 16383;
72 const unsigned int maxPrecision = 113;
73 const unsigned int maxPowerOfFiveExponent = maxExponent + maxPrecision - 1;
74 const unsigned int maxPowerOfFiveParts = 2 + ((maxPowerOfFiveExponent * 815)
75 / (351 * integerPartWidth));
78 /* Put a bunch of private, handy routines in an anonymous namespace. */
81 static inline unsigned int
82 partCountForBits(unsigned int bits)
84 return ((bits) + integerPartWidth - 1) / integerPartWidth;
87 /* Returns 0U-9U. Return values >= 10U are not digits. */
88 static inline unsigned int
89 decDigitValue(unsigned int c)
95 hexDigitValue(unsigned int c)
115 assertArithmeticOK(const llvm::fltSemantics &semantics) {
116 assert(semantics.arithmeticOK
117 && "Compile-time arithmetic does not support these semantics");
120 /* Return the value of a decimal exponent of the form
123 If the exponent overflows, returns a large exponent with the
126 readExponent(const char *p)
129 unsigned int absExponent;
130 const unsigned int overlargeExponent = 24000; /* FIXME. */
132 isNegative = (*p == '-');
133 if (*p == '-' || *p == '+')
136 absExponent = decDigitValue(*p++);
137 assert (absExponent < 10U);
142 value = decDigitValue(*p);
147 value += absExponent * 10;
148 if (absExponent >= overlargeExponent) {
149 absExponent = overlargeExponent;
156 return -(int) absExponent;
158 return (int) absExponent;
161 /* This is ugly and needs cleaning up, but I don't immediately see
162 how whilst remaining safe. */
164 totalExponent(const char *p, int exponentAdjustment)
166 int unsignedExponent;
167 bool negative, overflow;
170 /* Move past the exponent letter and sign to the digits. */
172 negative = *p == '-';
173 if(*p == '-' || *p == '+')
176 unsignedExponent = 0;
181 value = decDigitValue(*p);
186 unsignedExponent = unsignedExponent * 10 + value;
187 if(unsignedExponent > 65535)
191 if(exponentAdjustment > 65535 || exponentAdjustment < -65536)
195 exponent = unsignedExponent;
197 exponent = -exponent;
198 exponent += exponentAdjustment;
199 if(exponent > 65535 || exponent < -65536)
204 exponent = negative ? -65536: 65535;
210 skipLeadingZeroesAndAnyDot(const char *p, const char **dot)
225 /* Given a normal decimal floating point number of the form
229 where the decimal point and exponent are optional, fill out the
230 structure D. Exponent is appropriate if the significand is
231 treated as an integer, and normalizedExponent if the significand
232 is taken to have the decimal point after a single leading
235 If the value is zero, V->firstSigDigit points to a non-digit, and
236 the return exponent is zero.
239 const char *firstSigDigit;
240 const char *lastSigDigit;
242 int normalizedExponent;
246 interpretDecimal(const char *p, decimalInfo *D)
250 p = skipLeadingZeroesAndAnyDot (p, &dot);
252 D->firstSigDigit = p;
254 D->normalizedExponent = 0;
261 if (decDigitValue(*p) >= 10U)
266 /* If number is all zerooes accept any exponent. */
267 if (p != D->firstSigDigit) {
268 if (*p == 'e' || *p == 'E')
269 D->exponent = readExponent(p + 1);
271 /* Implied decimal point? */
275 /* Drop insignificant trailing zeroes. */
282 /* Adjust the exponents for any decimal point. */
283 D->exponent += static_cast<exponent_t>((dot - p) - (dot > p));
284 D->normalizedExponent = (D->exponent +
285 static_cast<exponent_t>((p - D->firstSigDigit)
286 - (dot > D->firstSigDigit && dot < p)));
292 /* Return the trailing fraction of a hexadecimal number.
293 DIGITVALUE is the first hex digit of the fraction, P points to
296 trailingHexadecimalFraction(const char *p, unsigned int digitValue)
298 unsigned int hexDigit;
300 /* If the first trailing digit isn't 0 or 8 we can work out the
301 fraction immediately. */
303 return lfMoreThanHalf;
304 else if(digitValue < 8 && digitValue > 0)
305 return lfLessThanHalf;
307 /* Otherwise we need to find the first non-zero digit. */
311 hexDigit = hexDigitValue(*p);
313 /* If we ran off the end it is exactly zero or one-half, otherwise
316 return digitValue == 0 ? lfExactlyZero: lfExactlyHalf;
318 return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
321 /* Return the fraction lost were a bignum truncated losing the least
322 significant BITS bits. */
324 lostFractionThroughTruncation(const integerPart *parts,
325 unsigned int partCount,
330 lsb = APInt::tcLSB(parts, partCount);
332 /* Note this is guaranteed true if bits == 0, or LSB == -1U. */
334 return lfExactlyZero;
336 return lfExactlyHalf;
337 if(bits <= partCount * integerPartWidth
338 && APInt::tcExtractBit(parts, bits - 1))
339 return lfMoreThanHalf;
341 return lfLessThanHalf;
344 /* Shift DST right BITS bits noting lost fraction. */
346 shiftRight(integerPart *dst, unsigned int parts, unsigned int bits)
348 lostFraction lost_fraction;
350 lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
352 APInt::tcShiftRight(dst, parts, bits);
354 return lost_fraction;
357 /* Combine the effect of two lost fractions. */
359 combineLostFractions(lostFraction moreSignificant,
360 lostFraction lessSignificant)
362 if(lessSignificant != lfExactlyZero) {
363 if(moreSignificant == lfExactlyZero)
364 moreSignificant = lfLessThanHalf;
365 else if(moreSignificant == lfExactlyHalf)
366 moreSignificant = lfMoreThanHalf;
369 return moreSignificant;
372 /* The error from the true value, in half-ulps, on multiplying two
373 floating point numbers, which differ from the value they
374 approximate by at most HUE1 and HUE2 half-ulps, is strictly less
375 than the returned value.
377 See "How to Read Floating Point Numbers Accurately" by William D
380 HUerrBound(bool inexactMultiply, unsigned int HUerr1, unsigned int HUerr2)
382 assert(HUerr1 < 2 || HUerr2 < 2 || (HUerr1 + HUerr2 < 8));
384 if (HUerr1 + HUerr2 == 0)
385 return inexactMultiply * 2; /* <= inexactMultiply half-ulps. */
387 return inexactMultiply + 2 * (HUerr1 + HUerr2);
390 /* The number of ulps from the boundary (zero, or half if ISNEAREST)
391 when the least significant BITS are truncated. BITS cannot be
394 ulpsFromBoundary(const integerPart *parts, unsigned int bits, bool isNearest)
396 unsigned int count, partBits;
397 integerPart part, boundary;
402 count = bits / integerPartWidth;
403 partBits = bits % integerPartWidth + 1;
405 part = parts[count] & (~(integerPart) 0 >> (integerPartWidth - partBits));
408 boundary = (integerPart) 1 << (partBits - 1);
413 if (part - boundary <= boundary - part)
414 return part - boundary;
416 return boundary - part;
419 if (part == boundary) {
422 return ~(integerPart) 0; /* A lot. */
425 } else if (part == boundary - 1) {
428 return ~(integerPart) 0; /* A lot. */
433 return ~(integerPart) 0; /* A lot. */
436 /* Place pow(5, power) in DST, and return the number of parts used.
437 DST must be at least one part larger than size of the answer. */
439 powerOf5(integerPart *dst, unsigned int power)
441 static const integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125,
443 static integerPart pow5s[maxPowerOfFiveParts * 2 + 5] = { 78125 * 5 };
444 static unsigned int partsCount[16] = { 1 };
446 integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5;
449 assert(power <= maxExponent);
454 *p1 = firstEightPowers[power & 7];
460 for (unsigned int n = 0; power; power >>= 1, n++) {
465 /* Calculate pow(5,pow(2,n+3)) if we haven't yet. */
467 pc = partsCount[n - 1];
468 APInt::tcFullMultiply(pow5, pow5 - pc, pow5 - pc, pc, pc);
470 if (pow5[pc - 1] == 0)
478 APInt::tcFullMultiply(p2, p1, pow5, result, pc);
480 if (p2[result - 1] == 0)
483 /* Now result is in p1 with partsCount parts and p2 is scratch
485 tmp = p1, p1 = p2, p2 = tmp;
492 APInt::tcAssign(dst, p1, result);
497 /* Zero at the end to avoid modular arithmetic when adding one; used
498 when rounding up during hexadecimal output. */
499 static const char hexDigitsLower[] = "0123456789abcdef0";
500 static const char hexDigitsUpper[] = "0123456789ABCDEF0";
501 static const char infinityL[] = "infinity";
502 static const char infinityU[] = "INFINITY";
503 static const char NaNL[] = "nan";
504 static const char NaNU[] = "NAN";
506 /* Write out an integerPart in hexadecimal, starting with the most
507 significant nibble. Write out exactly COUNT hexdigits, return
510 partAsHex (char *dst, integerPart part, unsigned int count,
511 const char *hexDigitChars)
513 unsigned int result = count;
515 assert (count != 0 && count <= integerPartWidth / 4);
517 part >>= (integerPartWidth - 4 * count);
519 dst[count] = hexDigitChars[part & 0xf];
526 /* Write out an unsigned decimal integer. */
528 writeUnsignedDecimal (char *dst, unsigned int n)
544 /* Write out a signed decimal integer. */
546 writeSignedDecimal (char *dst, int value)
550 dst = writeUnsignedDecimal(dst, -(unsigned) value);
552 dst = writeUnsignedDecimal(dst, value);
560 APFloat::initialize(const fltSemantics *ourSemantics)
564 semantics = ourSemantics;
567 significand.parts = new integerPart[count];
571 APFloat::freeSignificand()
574 delete [] significand.parts;
578 APFloat::assign(const APFloat &rhs)
580 assert(semantics == rhs.semantics);
583 category = rhs.category;
584 exponent = rhs.exponent;
586 exponent2 = rhs.exponent2;
587 if(category == fcNormal || category == fcNaN)
588 copySignificand(rhs);
592 APFloat::copySignificand(const APFloat &rhs)
594 assert(category == fcNormal || category == fcNaN);
595 assert(rhs.partCount() >= partCount());
597 APInt::tcAssign(significandParts(), rhs.significandParts(),
601 /* Make this number a NaN, with an arbitrary but deterministic value
602 for the significand. */
604 APFloat::makeNaN(void)
607 APInt::tcSet(significandParts(), ~0U, partCount());
611 APFloat::operator=(const APFloat &rhs)
614 if(semantics != rhs.semantics) {
616 initialize(rhs.semantics);
625 APFloat::bitwiseIsEqual(const APFloat &rhs) const {
628 if (semantics != rhs.semantics ||
629 category != rhs.category ||
632 if (semantics==(const llvm::fltSemantics*)&PPCDoubleDouble &&
635 if (category==fcZero || category==fcInfinity)
637 else if (category==fcNormal && exponent!=rhs.exponent)
639 else if (semantics==(const llvm::fltSemantics*)&PPCDoubleDouble &&
640 exponent2!=rhs.exponent2)
644 const integerPart* p=significandParts();
645 const integerPart* q=rhs.significandParts();
646 for (; i>0; i--, p++, q++) {
654 APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value)
656 assertArithmeticOK(ourSemantics);
657 initialize(&ourSemantics);
660 exponent = ourSemantics.precision - 1;
661 significandParts()[0] = value;
662 normalize(rmNearestTiesToEven, lfExactlyZero);
665 APFloat::APFloat(const fltSemantics &ourSemantics,
666 fltCategory ourCategory, bool negative)
668 assertArithmeticOK(ourSemantics);
669 initialize(&ourSemantics);
670 category = ourCategory;
672 if(category == fcNormal)
674 else if (ourCategory == fcNaN)
678 APFloat::APFloat(const fltSemantics &ourSemantics, const char *text)
680 assertArithmeticOK(ourSemantics);
681 initialize(&ourSemantics);
682 convertFromString(text, rmNearestTiesToEven);
685 APFloat::APFloat(const APFloat &rhs)
687 initialize(rhs.semantics);
696 // Profile - This method 'profiles' an APFloat for use with FoldingSet.
697 void APFloat::Profile(FoldingSetNodeID& ID) const {
698 ID.Add(bitcastToAPInt());
702 APFloat::partCount() const
704 return partCountForBits(semantics->precision + 1);
708 APFloat::semanticsPrecision(const fltSemantics &semantics)
710 return semantics.precision;
714 APFloat::significandParts() const
716 return const_cast<APFloat *>(this)->significandParts();
720 APFloat::significandParts()
722 assert(category == fcNormal || category == fcNaN);
725 return significand.parts;
727 return &significand.part;
731 APFloat::zeroSignificand()
734 APInt::tcSet(significandParts(), 0, partCount());
737 /* Increment an fcNormal floating point number's significand. */
739 APFloat::incrementSignificand()
743 carry = APInt::tcIncrement(significandParts(), partCount());
745 /* Our callers should never cause us to overflow. */
749 /* Add the significand of the RHS. Returns the carry flag. */
751 APFloat::addSignificand(const APFloat &rhs)
755 parts = significandParts();
757 assert(semantics == rhs.semantics);
758 assert(exponent == rhs.exponent);
760 return APInt::tcAdd(parts, rhs.significandParts(), 0, partCount());
763 /* Subtract the significand of the RHS with a borrow flag. Returns
766 APFloat::subtractSignificand(const APFloat &rhs, integerPart borrow)
770 parts = significandParts();
772 assert(semantics == rhs.semantics);
773 assert(exponent == rhs.exponent);
775 return APInt::tcSubtract(parts, rhs.significandParts(), borrow,
779 /* Multiply the significand of the RHS. If ADDEND is non-NULL, add it
780 on to the full-precision result of the multiplication. Returns the
783 APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
785 unsigned int omsb; // One, not zero, based MSB.
786 unsigned int partsCount, newPartsCount, precision;
787 integerPart *lhsSignificand;
788 integerPart scratch[4];
789 integerPart *fullSignificand;
790 lostFraction lost_fraction;
793 assert(semantics == rhs.semantics);
795 precision = semantics->precision;
796 newPartsCount = partCountForBits(precision * 2);
798 if(newPartsCount > 4)
799 fullSignificand = new integerPart[newPartsCount];
801 fullSignificand = scratch;
803 lhsSignificand = significandParts();
804 partsCount = partCount();
806 APInt::tcFullMultiply(fullSignificand, lhsSignificand,
807 rhs.significandParts(), partsCount, partsCount);
809 lost_fraction = lfExactlyZero;
810 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
811 exponent += rhs.exponent;
814 Significand savedSignificand = significand;
815 const fltSemantics *savedSemantics = semantics;
816 fltSemantics extendedSemantics;
818 unsigned int extendedPrecision;
820 /* Normalize our MSB. */
821 extendedPrecision = precision + precision - 1;
822 if(omsb != extendedPrecision)
824 APInt::tcShiftLeft(fullSignificand, newPartsCount,
825 extendedPrecision - omsb);
826 exponent -= extendedPrecision - omsb;
829 /* Create new semantics. */
830 extendedSemantics = *semantics;
831 extendedSemantics.precision = extendedPrecision;
833 if(newPartsCount == 1)
834 significand.part = fullSignificand[0];
836 significand.parts = fullSignificand;
837 semantics = &extendedSemantics;
839 APFloat extendedAddend(*addend);
840 status = extendedAddend.convert(extendedSemantics, rmTowardZero, &ignored);
841 assert(status == opOK);
842 lost_fraction = addOrSubtractSignificand(extendedAddend, false);
844 /* Restore our state. */
845 if(newPartsCount == 1)
846 fullSignificand[0] = significand.part;
847 significand = savedSignificand;
848 semantics = savedSemantics;
850 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
853 exponent -= (precision - 1);
855 if(omsb > precision) {
856 unsigned int bits, significantParts;
859 bits = omsb - precision;
860 significantParts = partCountForBits(omsb);
861 lf = shiftRight(fullSignificand, significantParts, bits);
862 lost_fraction = combineLostFractions(lf, lost_fraction);
866 APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
868 if(newPartsCount > 4)
869 delete [] fullSignificand;
871 return lost_fraction;
874 /* Multiply the significands of LHS and RHS to DST. */
876 APFloat::divideSignificand(const APFloat &rhs)
878 unsigned int bit, i, partsCount;
879 const integerPart *rhsSignificand;
880 integerPart *lhsSignificand, *dividend, *divisor;
881 integerPart scratch[4];
882 lostFraction lost_fraction;
884 assert(semantics == rhs.semantics);
886 lhsSignificand = significandParts();
887 rhsSignificand = rhs.significandParts();
888 partsCount = partCount();
891 dividend = new integerPart[partsCount * 2];
895 divisor = dividend + partsCount;
897 /* Copy the dividend and divisor as they will be modified in-place. */
898 for(i = 0; i < partsCount; i++) {
899 dividend[i] = lhsSignificand[i];
900 divisor[i] = rhsSignificand[i];
901 lhsSignificand[i] = 0;
904 exponent -= rhs.exponent;
906 unsigned int precision = semantics->precision;
908 /* Normalize the divisor. */
909 bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
912 APInt::tcShiftLeft(divisor, partsCount, bit);
915 /* Normalize the dividend. */
916 bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
919 APInt::tcShiftLeft(dividend, partsCount, bit);
922 /* Ensure the dividend >= divisor initially for the loop below.
923 Incidentally, this means that the division loop below is
924 guaranteed to set the integer bit to one. */
925 if(APInt::tcCompare(dividend, divisor, partsCount) < 0) {
927 APInt::tcShiftLeft(dividend, partsCount, 1);
928 assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0);
932 for(bit = precision; bit; bit -= 1) {
933 if(APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
934 APInt::tcSubtract(dividend, divisor, 0, partsCount);
935 APInt::tcSetBit(lhsSignificand, bit - 1);
938 APInt::tcShiftLeft(dividend, partsCount, 1);
941 /* Figure out the lost fraction. */
942 int cmp = APInt::tcCompare(dividend, divisor, partsCount);
945 lost_fraction = lfMoreThanHalf;
947 lost_fraction = lfExactlyHalf;
948 else if(APInt::tcIsZero(dividend, partsCount))
949 lost_fraction = lfExactlyZero;
951 lost_fraction = lfLessThanHalf;
956 return lost_fraction;
960 APFloat::significandMSB() const
962 return APInt::tcMSB(significandParts(), partCount());
966 APFloat::significandLSB() const
968 return APInt::tcLSB(significandParts(), partCount());
971 /* Note that a zero result is NOT normalized to fcZero. */
973 APFloat::shiftSignificandRight(unsigned int bits)
975 /* Our exponent should not overflow. */
976 assert((exponent_t) (exponent + bits) >= exponent);
980 return shiftRight(significandParts(), partCount(), bits);
983 /* Shift the significand left BITS bits, subtract BITS from its exponent. */
985 APFloat::shiftSignificandLeft(unsigned int bits)
987 assert(bits < semantics->precision);
990 unsigned int partsCount = partCount();
992 APInt::tcShiftLeft(significandParts(), partsCount, bits);
995 assert(!APInt::tcIsZero(significandParts(), partsCount));
1000 APFloat::compareAbsoluteValue(const APFloat &rhs) const
1004 assert(semantics == rhs.semantics);
1005 assert(category == fcNormal);
1006 assert(rhs.category == fcNormal);
1008 compare = exponent - rhs.exponent;
1010 /* If exponents are equal, do an unsigned bignum comparison of the
1013 compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
1017 return cmpGreaterThan;
1018 else if(compare < 0)
1024 /* Handle overflow. Sign is preserved. We either become infinity or
1025 the largest finite number. */
1027 APFloat::handleOverflow(roundingMode rounding_mode)
1030 if(rounding_mode == rmNearestTiesToEven
1031 || rounding_mode == rmNearestTiesToAway
1032 || (rounding_mode == rmTowardPositive && !sign)
1033 || (rounding_mode == rmTowardNegative && sign))
1035 category = fcInfinity;
1036 return (opStatus) (opOverflow | opInexact);
1039 /* Otherwise we become the largest finite number. */
1040 category = fcNormal;
1041 exponent = semantics->maxExponent;
1042 APInt::tcSetLeastSignificantBits(significandParts(), partCount(),
1043 semantics->precision);
1048 /* Returns TRUE if, when truncating the current number, with BIT the
1049 new LSB, with the given lost fraction and rounding mode, the result
1050 would need to be rounded away from zero (i.e., by increasing the
1051 signficand). This routine must work for fcZero of both signs, and
1052 fcNormal numbers. */
1054 APFloat::roundAwayFromZero(roundingMode rounding_mode,
1055 lostFraction lost_fraction,
1056 unsigned int bit) const
1058 /* NaNs and infinities should not have lost fractions. */
1059 assert(category == fcNormal || category == fcZero);
1061 /* Current callers never pass this so we don't handle it. */
1062 assert(lost_fraction != lfExactlyZero);
1064 switch(rounding_mode) {
1068 case rmNearestTiesToAway:
1069 return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
1071 case rmNearestTiesToEven:
1072 if(lost_fraction == lfMoreThanHalf)
1075 /* Our zeroes don't have a significand to test. */
1076 if(lost_fraction == lfExactlyHalf && category != fcZero)
1077 return APInt::tcExtractBit(significandParts(), bit);
1084 case rmTowardPositive:
1085 return sign == false;
1087 case rmTowardNegative:
1088 return sign == true;
1093 APFloat::normalize(roundingMode rounding_mode,
1094 lostFraction lost_fraction)
1096 unsigned int omsb; /* One, not zero, based MSB. */
1099 if(category != fcNormal)
1102 /* Before rounding normalize the exponent of fcNormal numbers. */
1103 omsb = significandMSB() + 1;
1106 /* OMSB is numbered from 1. We want to place it in the integer
1107 bit numbered PRECISON if possible, with a compensating change in
1109 exponentChange = omsb - semantics->precision;
1111 /* If the resulting exponent is too high, overflow according to
1112 the rounding mode. */
1113 if(exponent + exponentChange > semantics->maxExponent)
1114 return handleOverflow(rounding_mode);
1116 /* Subnormal numbers have exponent minExponent, and their MSB
1117 is forced based on that. */
1118 if(exponent + exponentChange < semantics->minExponent)
1119 exponentChange = semantics->minExponent - exponent;
1121 /* Shifting left is easy as we don't lose precision. */
1122 if(exponentChange < 0) {
1123 assert(lost_fraction == lfExactlyZero);
1125 shiftSignificandLeft(-exponentChange);
1130 if(exponentChange > 0) {
1133 /* Shift right and capture any new lost fraction. */
1134 lf = shiftSignificandRight(exponentChange);
1136 lost_fraction = combineLostFractions(lf, lost_fraction);
1138 /* Keep OMSB up-to-date. */
1139 if(omsb > (unsigned) exponentChange)
1140 omsb -= exponentChange;
1146 /* Now round the number according to rounding_mode given the lost
1149 /* As specified in IEEE 754, since we do not trap we do not report
1150 underflow for exact results. */
1151 if(lost_fraction == lfExactlyZero) {
1152 /* Canonicalize zeroes. */
1159 /* Increment the significand if we're rounding away from zero. */
1160 if(roundAwayFromZero(rounding_mode, lost_fraction, 0)) {
1162 exponent = semantics->minExponent;
1164 incrementSignificand();
1165 omsb = significandMSB() + 1;
1167 /* Did the significand increment overflow? */
1168 if(omsb == (unsigned) semantics->precision + 1) {
1169 /* Renormalize by incrementing the exponent and shifting our
1170 significand right one. However if we already have the
1171 maximum exponent we overflow to infinity. */
1172 if(exponent == semantics->maxExponent) {
1173 category = fcInfinity;
1175 return (opStatus) (opOverflow | opInexact);
1178 shiftSignificandRight(1);
1184 /* The normal case - we were and are not denormal, and any
1185 significand increment above didn't overflow. */
1186 if(omsb == semantics->precision)
1189 /* We have a non-zero denormal. */
1190 assert(omsb < semantics->precision);
1192 /* Canonicalize zeroes. */
1196 /* The fcZero case is a denormal that underflowed to zero. */
1197 return (opStatus) (opUnderflow | opInexact);
1201 APFloat::addOrSubtractSpecials(const APFloat &rhs, bool subtract)
1203 switch(convolve(category, rhs.category)) {
1207 case convolve(fcNaN, fcZero):
1208 case convolve(fcNaN, fcNormal):
1209 case convolve(fcNaN, fcInfinity):
1210 case convolve(fcNaN, fcNaN):
1211 case convolve(fcNormal, fcZero):
1212 case convolve(fcInfinity, fcNormal):
1213 case convolve(fcInfinity, fcZero):
1216 case convolve(fcZero, fcNaN):
1217 case convolve(fcNormal, fcNaN):
1218 case convolve(fcInfinity, fcNaN):
1220 copySignificand(rhs);
1223 case convolve(fcNormal, fcInfinity):
1224 case convolve(fcZero, fcInfinity):
1225 category = fcInfinity;
1226 sign = rhs.sign ^ subtract;
1229 case convolve(fcZero, fcNormal):
1231 sign = rhs.sign ^ subtract;
1234 case convolve(fcZero, fcZero):
1235 /* Sign depends on rounding mode; handled by caller. */
1238 case convolve(fcInfinity, fcInfinity):
1239 /* Differently signed infinities can only be validly
1241 if((sign ^ rhs.sign) != subtract) {
1248 case convolve(fcNormal, fcNormal):
1253 /* Add or subtract two normal numbers. */
1255 APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
1258 lostFraction lost_fraction;
1261 /* Determine if the operation on the absolute values is effectively
1262 an addition or subtraction. */
1263 subtract ^= (sign ^ rhs.sign) ? true : false;
1265 /* Are we bigger exponent-wise than the RHS? */
1266 bits = exponent - rhs.exponent;
1268 /* Subtraction is more subtle than one might naively expect. */
1270 APFloat temp_rhs(rhs);
1274 reverse = compareAbsoluteValue(temp_rhs) == cmpLessThan;
1275 lost_fraction = lfExactlyZero;
1276 } else if (bits > 0) {
1277 lost_fraction = temp_rhs.shiftSignificandRight(bits - 1);
1278 shiftSignificandLeft(1);
1281 lost_fraction = shiftSignificandRight(-bits - 1);
1282 temp_rhs.shiftSignificandLeft(1);
1287 carry = temp_rhs.subtractSignificand
1288 (*this, lost_fraction != lfExactlyZero);
1289 copySignificand(temp_rhs);
1292 carry = subtractSignificand
1293 (temp_rhs, lost_fraction != lfExactlyZero);
1296 /* Invert the lost fraction - it was on the RHS and
1298 if(lost_fraction == lfLessThanHalf)
1299 lost_fraction = lfMoreThanHalf;
1300 else if(lost_fraction == lfMoreThanHalf)
1301 lost_fraction = lfLessThanHalf;
1303 /* The code above is intended to ensure that no borrow is
1308 APFloat temp_rhs(rhs);
1310 lost_fraction = temp_rhs.shiftSignificandRight(bits);
1311 carry = addSignificand(temp_rhs);
1313 lost_fraction = shiftSignificandRight(-bits);
1314 carry = addSignificand(rhs);
1317 /* We have a guard bit; generating a carry cannot happen. */
1321 return lost_fraction;
1325 APFloat::multiplySpecials(const APFloat &rhs)
1327 switch(convolve(category, rhs.category)) {
1331 case convolve(fcNaN, fcZero):
1332 case convolve(fcNaN, fcNormal):
1333 case convolve(fcNaN, fcInfinity):
1334 case convolve(fcNaN, fcNaN):
1337 case convolve(fcZero, fcNaN):
1338 case convolve(fcNormal, fcNaN):
1339 case convolve(fcInfinity, fcNaN):
1341 copySignificand(rhs);
1344 case convolve(fcNormal, fcInfinity):
1345 case convolve(fcInfinity, fcNormal):
1346 case convolve(fcInfinity, fcInfinity):
1347 category = fcInfinity;
1350 case convolve(fcZero, fcNormal):
1351 case convolve(fcNormal, fcZero):
1352 case convolve(fcZero, fcZero):
1356 case convolve(fcZero, fcInfinity):
1357 case convolve(fcInfinity, fcZero):
1361 case convolve(fcNormal, fcNormal):
1367 APFloat::divideSpecials(const APFloat &rhs)
1369 switch(convolve(category, rhs.category)) {
1373 case convolve(fcNaN, fcZero):
1374 case convolve(fcNaN, fcNormal):
1375 case convolve(fcNaN, fcInfinity):
1376 case convolve(fcNaN, fcNaN):
1377 case convolve(fcInfinity, fcZero):
1378 case convolve(fcInfinity, fcNormal):
1379 case convolve(fcZero, fcInfinity):
1380 case convolve(fcZero, fcNormal):
1383 case convolve(fcZero, fcNaN):
1384 case convolve(fcNormal, fcNaN):
1385 case convolve(fcInfinity, fcNaN):
1387 copySignificand(rhs);
1390 case convolve(fcNormal, fcInfinity):
1394 case convolve(fcNormal, fcZero):
1395 category = fcInfinity;
1398 case convolve(fcInfinity, fcInfinity):
1399 case convolve(fcZero, fcZero):
1403 case convolve(fcNormal, fcNormal):
1410 APFloat::changeSign()
1412 /* Look mummy, this one's easy. */
1417 APFloat::clearSign()
1419 /* So is this one. */
1424 APFloat::copySign(const APFloat &rhs)
1430 /* Normalized addition or subtraction. */
1432 APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
1437 assertArithmeticOK(*semantics);
1439 fs = addOrSubtractSpecials(rhs, subtract);
1441 /* This return code means it was not a simple case. */
1442 if(fs == opDivByZero) {
1443 lostFraction lost_fraction;
1445 lost_fraction = addOrSubtractSignificand(rhs, subtract);
1446 fs = normalize(rounding_mode, lost_fraction);
1448 /* Can only be zero if we lost no fraction. */
1449 assert(category != fcZero || lost_fraction == lfExactlyZero);
1452 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1453 positive zero unless rounding to minus infinity, except that
1454 adding two like-signed zeroes gives that zero. */
1455 if(category == fcZero) {
1456 if(rhs.category != fcZero || (sign == rhs.sign) == subtract)
1457 sign = (rounding_mode == rmTowardNegative);
1463 /* Normalized addition. */
1465 APFloat::add(const APFloat &rhs, roundingMode rounding_mode)
1467 return addOrSubtract(rhs, rounding_mode, false);
1470 /* Normalized subtraction. */
1472 APFloat::subtract(const APFloat &rhs, roundingMode rounding_mode)
1474 return addOrSubtract(rhs, rounding_mode, true);
1477 /* Normalized multiply. */
1479 APFloat::multiply(const APFloat &rhs, roundingMode rounding_mode)
1483 assertArithmeticOK(*semantics);
1485 fs = multiplySpecials(rhs);
1487 if(category == fcNormal) {
1488 lostFraction lost_fraction = multiplySignificand(rhs, 0);
1489 fs = normalize(rounding_mode, lost_fraction);
1490 if(lost_fraction != lfExactlyZero)
1491 fs = (opStatus) (fs | opInexact);
1497 /* Normalized divide. */
1499 APFloat::divide(const APFloat &rhs, roundingMode rounding_mode)
1503 assertArithmeticOK(*semantics);
1505 fs = divideSpecials(rhs);
1507 if(category == fcNormal) {
1508 lostFraction lost_fraction = divideSignificand(rhs);
1509 fs = normalize(rounding_mode, lost_fraction);
1510 if(lost_fraction != lfExactlyZero)
1511 fs = (opStatus) (fs | opInexact);
1517 /* Normalized remainder. This is not currently doing TRT. */
1519 APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
1523 unsigned int origSign = sign;
1525 assertArithmeticOK(*semantics);
1526 fs = V.divide(rhs, rmNearestTiesToEven);
1527 if (fs == opDivByZero)
1530 int parts = partCount();
1531 integerPart *x = new integerPart[parts];
1533 fs = V.convertToInteger(x, parts * integerPartWidth, true,
1534 rmNearestTiesToEven, &ignored);
1535 if (fs==opInvalidOp)
1538 fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
1539 rmNearestTiesToEven);
1540 assert(fs==opOK); // should always work
1542 fs = V.multiply(rhs, rounding_mode);
1543 assert(fs==opOK || fs==opInexact); // should not overflow or underflow
1545 fs = subtract(V, rounding_mode);
1546 assert(fs==opOK || fs==opInexact); // likewise
1549 sign = origSign; // IEEE754 requires this
1554 /* Normalized fused-multiply-add. */
1556 APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
1557 const APFloat &addend,
1558 roundingMode rounding_mode)
1562 assertArithmeticOK(*semantics);
1564 /* Post-multiplication sign, before addition. */
1565 sign ^= multiplicand.sign;
1567 /* If and only if all arguments are normal do we need to do an
1568 extended-precision calculation. */
1569 if(category == fcNormal
1570 && multiplicand.category == fcNormal
1571 && addend.category == fcNormal) {
1572 lostFraction lost_fraction;
1574 lost_fraction = multiplySignificand(multiplicand, &addend);
1575 fs = normalize(rounding_mode, lost_fraction);
1576 if(lost_fraction != lfExactlyZero)
1577 fs = (opStatus) (fs | opInexact);
1579 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1580 positive zero unless rounding to minus infinity, except that
1581 adding two like-signed zeroes gives that zero. */
1582 if(category == fcZero && sign != addend.sign)
1583 sign = (rounding_mode == rmTowardNegative);
1585 fs = multiplySpecials(multiplicand);
1587 /* FS can only be opOK or opInvalidOp. There is no more work
1588 to do in the latter case. The IEEE-754R standard says it is
1589 implementation-defined in this case whether, if ADDEND is a
1590 quiet NaN, we raise invalid op; this implementation does so.
1592 If we need to do the addition we can do so with normal
1595 fs = addOrSubtract(addend, rounding_mode, false);
1601 /* Comparison requires normalized numbers. */
1603 APFloat::compare(const APFloat &rhs) const
1607 assertArithmeticOK(*semantics);
1608 assert(semantics == rhs.semantics);
1610 switch(convolve(category, rhs.category)) {
1614 case convolve(fcNaN, fcZero):
1615 case convolve(fcNaN, fcNormal):
1616 case convolve(fcNaN, fcInfinity):
1617 case convolve(fcNaN, fcNaN):
1618 case convolve(fcZero, fcNaN):
1619 case convolve(fcNormal, fcNaN):
1620 case convolve(fcInfinity, fcNaN):
1621 return cmpUnordered;
1623 case convolve(fcInfinity, fcNormal):
1624 case convolve(fcInfinity, fcZero):
1625 case convolve(fcNormal, fcZero):
1629 return cmpGreaterThan;
1631 case convolve(fcNormal, fcInfinity):
1632 case convolve(fcZero, fcInfinity):
1633 case convolve(fcZero, fcNormal):
1635 return cmpGreaterThan;
1639 case convolve(fcInfinity, fcInfinity):
1640 if(sign == rhs.sign)
1645 return cmpGreaterThan;
1647 case convolve(fcZero, fcZero):
1650 case convolve(fcNormal, fcNormal):
1654 /* Two normal numbers. Do they have the same sign? */
1655 if(sign != rhs.sign) {
1657 result = cmpLessThan;
1659 result = cmpGreaterThan;
1661 /* Compare absolute values; invert result if negative. */
1662 result = compareAbsoluteValue(rhs);
1665 if(result == cmpLessThan)
1666 result = cmpGreaterThan;
1667 else if(result == cmpGreaterThan)
1668 result = cmpLessThan;
1675 /// APFloat::convert - convert a value of one floating point type to another.
1676 /// The return value corresponds to the IEEE754 exceptions. *losesInfo
1677 /// records whether the transformation lost information, i.e. whether
1678 /// converting the result back to the original type will produce the
1679 /// original value (this is almost the same as return value==fsOK, but there
1680 /// are edge cases where this is not so).
1683 APFloat::convert(const fltSemantics &toSemantics,
1684 roundingMode rounding_mode, bool *losesInfo)
1686 lostFraction lostFraction;
1687 unsigned int newPartCount, oldPartCount;
1690 assertArithmeticOK(*semantics);
1691 assertArithmeticOK(toSemantics);
1692 lostFraction = lfExactlyZero;
1693 newPartCount = partCountForBits(toSemantics.precision + 1);
1694 oldPartCount = partCount();
1696 /* Handle storage complications. If our new form is wider,
1697 re-allocate our bit pattern into wider storage. If it is
1698 narrower, we ignore the excess parts, but if narrowing to a
1699 single part we need to free the old storage.
1700 Be careful not to reference significandParts for zeroes
1701 and infinities, since it aborts. */
1702 if (newPartCount > oldPartCount) {
1703 integerPart *newParts;
1704 newParts = new integerPart[newPartCount];
1705 APInt::tcSet(newParts, 0, newPartCount);
1706 if (category==fcNormal || category==fcNaN)
1707 APInt::tcAssign(newParts, significandParts(), oldPartCount);
1709 significand.parts = newParts;
1710 } else if (newPartCount < oldPartCount) {
1711 /* Capture any lost fraction through truncation of parts so we get
1712 correct rounding whilst normalizing. */
1713 if (category==fcNormal)
1714 lostFraction = lostFractionThroughTruncation
1715 (significandParts(), oldPartCount, toSemantics.precision);
1716 if (newPartCount == 1) {
1717 integerPart newPart = 0;
1718 if (category==fcNormal || category==fcNaN)
1719 newPart = significandParts()[0];
1721 significand.part = newPart;
1725 if(category == fcNormal) {
1726 /* Re-interpret our bit-pattern. */
1727 exponent += toSemantics.precision - semantics->precision;
1728 semantics = &toSemantics;
1729 fs = normalize(rounding_mode, lostFraction);
1730 *losesInfo = (fs != opOK);
1731 } else if (category == fcNaN) {
1732 int shift = toSemantics.precision - semantics->precision;
1733 // Do this now so significandParts gets the right answer
1734 const fltSemantics *oldSemantics = semantics;
1735 semantics = &toSemantics;
1737 // No normalization here, just truncate
1739 APInt::tcShiftLeft(significandParts(), newPartCount, shift);
1740 else if (shift < 0) {
1741 unsigned ushift = -shift;
1742 // Figure out if we are losing information. This happens
1743 // if are shifting out something other than 0s, or if the x87 long
1744 // double input did not have its integer bit set (pseudo-NaN), or if the
1745 // x87 long double input did not have its QNan bit set (because the x87
1746 // hardware sets this bit when converting a lower-precision NaN to
1747 // x87 long double).
1748 if (APInt::tcLSB(significandParts(), newPartCount) < ushift)
1750 if (oldSemantics == &APFloat::x87DoubleExtended &&
1751 (!(*significandParts() & 0x8000000000000000ULL) ||
1752 !(*significandParts() & 0x4000000000000000ULL)))
1754 APInt::tcShiftRight(significandParts(), newPartCount, ushift);
1756 // gcc forces the Quiet bit on, which means (float)(double)(float_sNan)
1757 // does not give you back the same bits. This is dubious, and we
1758 // don't currently do it. You're really supposed to get
1759 // an invalid operation signal at runtime, but nobody does that.
1762 semantics = &toSemantics;
1770 /* Convert a floating point number to an integer according to the
1771 rounding mode. If the rounded integer value is out of range this
1772 returns an invalid operation exception and the contents of the
1773 destination parts are unspecified. If the rounded value is in
1774 range but the floating point number is not the exact integer, the C
1775 standard doesn't require an inexact exception to be raised. IEEE
1776 854 does require it so we do that.
1778 Note that for conversions to integer type the C standard requires
1779 round-to-zero to always be used. */
1781 APFloat::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
1783 roundingMode rounding_mode,
1784 bool *isExact) const
1786 lostFraction lost_fraction;
1787 const integerPart *src;
1788 unsigned int dstPartsCount, truncatedBits;
1790 assertArithmeticOK(*semantics);
1794 /* Handle the three special cases first. */
1795 if(category == fcInfinity || category == fcNaN)
1798 dstPartsCount = partCountForBits(width);
1800 if(category == fcZero) {
1801 APInt::tcSet(parts, 0, dstPartsCount);
1802 // Negative zero can't be represented as an int.
1807 src = significandParts();
1809 /* Step 1: place our absolute value, with any fraction truncated, in
1812 /* Our absolute value is less than one; truncate everything. */
1813 APInt::tcSet(parts, 0, dstPartsCount);
1814 truncatedBits = semantics->precision;
1816 /* We want the most significant (exponent + 1) bits; the rest are
1818 unsigned int bits = exponent + 1U;
1820 /* Hopelessly large in magnitude? */
1824 if (bits < semantics->precision) {
1825 /* We truncate (semantics->precision - bits) bits. */
1826 truncatedBits = semantics->precision - bits;
1827 APInt::tcExtract(parts, dstPartsCount, src, bits, truncatedBits);
1829 /* We want at least as many bits as are available. */
1830 APInt::tcExtract(parts, dstPartsCount, src, semantics->precision, 0);
1831 APInt::tcShiftLeft(parts, dstPartsCount, bits - semantics->precision);
1836 /* Step 2: work out any lost fraction, and increment the absolute
1837 value if we would round away from zero. */
1838 if (truncatedBits) {
1839 lost_fraction = lostFractionThroughTruncation(src, partCount(),
1841 if (lost_fraction != lfExactlyZero
1842 && roundAwayFromZero(rounding_mode, lost_fraction, truncatedBits)) {
1843 if (APInt::tcIncrement(parts, dstPartsCount))
1844 return opInvalidOp; /* Overflow. */
1847 lost_fraction = lfExactlyZero;
1850 /* Step 3: check if we fit in the destination. */
1851 unsigned int omsb = APInt::tcMSB(parts, dstPartsCount) + 1;
1855 /* Negative numbers cannot be represented as unsigned. */
1859 /* It takes omsb bits to represent the unsigned integer value.
1860 We lose a bit for the sign, but care is needed as the
1861 maximally negative integer is a special case. */
1862 if (omsb == width && APInt::tcLSB(parts, dstPartsCount) + 1 != omsb)
1865 /* This case can happen because of rounding. */
1870 APInt::tcNegate (parts, dstPartsCount);
1872 if (omsb >= width + !isSigned)
1876 if (lost_fraction == lfExactlyZero) {
1883 /* Same as convertToSignExtendedInteger, except we provide
1884 deterministic values in case of an invalid operation exception,
1885 namely zero for NaNs and the minimal or maximal value respectively
1886 for underflow or overflow.
1887 The *isExact output tells whether the result is exact, in the sense
1888 that converting it back to the original floating point type produces
1889 the original value. This is almost equivalent to result==opOK,
1890 except for negative zeroes.
1893 APFloat::convertToInteger(integerPart *parts, unsigned int width,
1895 roundingMode rounding_mode, bool *isExact) const
1899 fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode,
1902 if (fs == opInvalidOp) {
1903 unsigned int bits, dstPartsCount;
1905 dstPartsCount = partCountForBits(width);
1907 if (category == fcNaN)
1912 bits = width - isSigned;
1914 APInt::tcSetLeastSignificantBits(parts, dstPartsCount, bits);
1915 if (sign && isSigned)
1916 APInt::tcShiftLeft(parts, dstPartsCount, width - 1);
1922 /* Convert an unsigned integer SRC to a floating point number,
1923 rounding according to ROUNDING_MODE. The sign of the floating
1924 point number is not modified. */
1926 APFloat::convertFromUnsignedParts(const integerPart *src,
1927 unsigned int srcCount,
1928 roundingMode rounding_mode)
1930 unsigned int omsb, precision, dstCount;
1932 lostFraction lost_fraction;
1934 assertArithmeticOK(*semantics);
1935 category = fcNormal;
1936 omsb = APInt::tcMSB(src, srcCount) + 1;
1937 dst = significandParts();
1938 dstCount = partCount();
1939 precision = semantics->precision;
1941 /* We want the most significant PRECISON bits of SRC. There may not
1942 be that many; extract what we can. */
1943 if (precision <= omsb) {
1944 exponent = omsb - 1;
1945 lost_fraction = lostFractionThroughTruncation(src, srcCount,
1947 APInt::tcExtract(dst, dstCount, src, precision, omsb - precision);
1949 exponent = precision - 1;
1950 lost_fraction = lfExactlyZero;
1951 APInt::tcExtract(dst, dstCount, src, omsb, 0);
1954 return normalize(rounding_mode, lost_fraction);
1958 APFloat::convertFromAPInt(const APInt &Val,
1960 roundingMode rounding_mode)
1962 unsigned int partCount = Val.getNumWords();
1966 if (isSigned && api.isNegative()) {
1971 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
1974 /* Convert a two's complement integer SRC to a floating point number,
1975 rounding according to ROUNDING_MODE. ISSIGNED is true if the
1976 integer is signed, in which case it must be sign-extended. */
1978 APFloat::convertFromSignExtendedInteger(const integerPart *src,
1979 unsigned int srcCount,
1981 roundingMode rounding_mode)
1985 assertArithmeticOK(*semantics);
1987 && APInt::tcExtractBit(src, srcCount * integerPartWidth - 1)) {
1990 /* If we're signed and negative negate a copy. */
1992 copy = new integerPart[srcCount];
1993 APInt::tcAssign(copy, src, srcCount);
1994 APInt::tcNegate(copy, srcCount);
1995 status = convertFromUnsignedParts(copy, srcCount, rounding_mode);
1999 status = convertFromUnsignedParts(src, srcCount, rounding_mode);
2005 /* FIXME: should this just take a const APInt reference? */
2007 APFloat::convertFromZeroExtendedInteger(const integerPart *parts,
2008 unsigned int width, bool isSigned,
2009 roundingMode rounding_mode)
2011 unsigned int partCount = partCountForBits(width);
2012 APInt api = APInt(width, partCount, parts);
2015 if(isSigned && APInt::tcExtractBit(parts, width - 1)) {
2020 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
2024 APFloat::convertFromHexadecimalString(const char *p,
2025 roundingMode rounding_mode)
2027 lostFraction lost_fraction;
2028 integerPart *significand;
2029 unsigned int bitPos, partsCount;
2030 const char *dot, *firstSignificantDigit;
2034 category = fcNormal;
2036 significand = significandParts();
2037 partsCount = partCount();
2038 bitPos = partsCount * integerPartWidth;
2040 /* Skip leading zeroes and any (hexa)decimal point. */
2041 p = skipLeadingZeroesAndAnyDot(p, &dot);
2042 firstSignificantDigit = p;
2045 integerPart hex_value;
2052 hex_value = hexDigitValue(*p);
2053 if(hex_value == -1U) {
2054 lost_fraction = lfExactlyZero;
2060 /* Store the number whilst 4-bit nibbles remain. */
2063 hex_value <<= bitPos % integerPartWidth;
2064 significand[bitPos / integerPartWidth] |= hex_value;
2066 lost_fraction = trailingHexadecimalFraction(p, hex_value);
2067 while(hexDigitValue(*p) != -1U)
2073 /* Hex floats require an exponent but not a hexadecimal point. */
2074 assert(*p == 'p' || *p == 'P');
2076 /* Ignore the exponent if we are zero. */
2077 if(p != firstSignificantDigit) {
2080 /* Implicit hexadecimal point? */
2084 /* Calculate the exponent adjustment implicit in the number of
2085 significant digits. */
2086 expAdjustment = static_cast<int>(dot - firstSignificantDigit);
2087 if(expAdjustment < 0)
2089 expAdjustment = expAdjustment * 4 - 1;
2091 /* Adjust for writing the significand starting at the most
2092 significant nibble. */
2093 expAdjustment += semantics->precision;
2094 expAdjustment -= partsCount * integerPartWidth;
2096 /* Adjust for the given exponent. */
2097 exponent = totalExponent(p, expAdjustment);
2100 return normalize(rounding_mode, lost_fraction);
2104 APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
2105 unsigned sigPartCount, int exp,
2106 roundingMode rounding_mode)
2108 unsigned int parts, pow5PartCount;
2109 fltSemantics calcSemantics = { 32767, -32767, 0, true };
2110 integerPart pow5Parts[maxPowerOfFiveParts];
2113 isNearest = (rounding_mode == rmNearestTiesToEven
2114 || rounding_mode == rmNearestTiesToAway);
2116 parts = partCountForBits(semantics->precision + 11);
2118 /* Calculate pow(5, abs(exp)). */
2119 pow5PartCount = powerOf5(pow5Parts, exp >= 0 ? exp: -exp);
2121 for (;; parts *= 2) {
2122 opStatus sigStatus, powStatus;
2123 unsigned int excessPrecision, truncatedBits;
2125 calcSemantics.precision = parts * integerPartWidth - 1;
2126 excessPrecision = calcSemantics.precision - semantics->precision;
2127 truncatedBits = excessPrecision;
2129 APFloat decSig(calcSemantics, fcZero, sign);
2130 APFloat pow5(calcSemantics, fcZero, false);
2132 sigStatus = decSig.convertFromUnsignedParts(decSigParts, sigPartCount,
2133 rmNearestTiesToEven);
2134 powStatus = pow5.convertFromUnsignedParts(pow5Parts, pow5PartCount,
2135 rmNearestTiesToEven);
2136 /* Add exp, as 10^n = 5^n * 2^n. */
2137 decSig.exponent += exp;
2139 lostFraction calcLostFraction;
2140 integerPart HUerr, HUdistance;
2141 unsigned int powHUerr;
2144 /* multiplySignificand leaves the precision-th bit set to 1. */
2145 calcLostFraction = decSig.multiplySignificand(pow5, NULL);
2146 powHUerr = powStatus != opOK;
2148 calcLostFraction = decSig.divideSignificand(pow5);
2149 /* Denormal numbers have less precision. */
2150 if (decSig.exponent < semantics->minExponent) {
2151 excessPrecision += (semantics->minExponent - decSig.exponent);
2152 truncatedBits = excessPrecision;
2153 if (excessPrecision > calcSemantics.precision)
2154 excessPrecision = calcSemantics.precision;
2156 /* Extra half-ulp lost in reciprocal of exponent. */
2157 powHUerr = (powStatus == opOK && calcLostFraction == lfExactlyZero) ? 0:2;
2160 /* Both multiplySignificand and divideSignificand return the
2161 result with the integer bit set. */
2162 assert (APInt::tcExtractBit
2163 (decSig.significandParts(), calcSemantics.precision - 1) == 1);
2165 HUerr = HUerrBound(calcLostFraction != lfExactlyZero, sigStatus != opOK,
2167 HUdistance = 2 * ulpsFromBoundary(decSig.significandParts(),
2168 excessPrecision, isNearest);
2170 /* Are we guaranteed to round correctly if we truncate? */
2171 if (HUdistance >= HUerr) {
2172 APInt::tcExtract(significandParts(), partCount(), decSig.significandParts(),
2173 calcSemantics.precision - excessPrecision,
2175 /* Take the exponent of decSig. If we tcExtract-ed less bits
2176 above we must adjust our exponent to compensate for the
2177 implicit right shift. */
2178 exponent = (decSig.exponent + semantics->precision
2179 - (calcSemantics.precision - excessPrecision));
2180 calcLostFraction = lostFractionThroughTruncation(decSig.significandParts(),
2183 return normalize(rounding_mode, calcLostFraction);
2189 APFloat::convertFromDecimalString(const char *p, roundingMode rounding_mode)
2194 /* Scan the text. */
2195 interpretDecimal(p, &D);
2197 /* Handle the quick cases. First the case of no significant digits,
2198 i.e. zero, and then exponents that are obviously too large or too
2199 small. Writing L for log 10 / log 2, a number d.ddddd*10^exp
2200 definitely overflows if
2202 (exp - 1) * L >= maxExponent
2204 and definitely underflows to zero where
2206 (exp + 1) * L <= minExponent - precision
2208 With integer arithmetic the tightest bounds for L are
2210 93/28 < L < 196/59 [ numerator <= 256 ]
2211 42039/12655 < L < 28738/8651 [ numerator <= 65536 ]
2214 if (decDigitValue(*D.firstSigDigit) >= 10U) {
2217 } else if ((D.normalizedExponent + 1) * 28738
2218 <= 8651 * (semantics->minExponent - (int) semantics->precision)) {
2219 /* Underflow to zero and round. */
2221 fs = normalize(rounding_mode, lfLessThanHalf);
2222 } else if ((D.normalizedExponent - 1) * 42039
2223 >= 12655 * semantics->maxExponent) {
2224 /* Overflow and round. */
2225 fs = handleOverflow(rounding_mode);
2227 integerPart *decSignificand;
2228 unsigned int partCount;
2230 /* A tight upper bound on number of bits required to hold an
2231 N-digit decimal integer is N * 196 / 59. Allocate enough space
2232 to hold the full significand, and an extra part required by
2234 partCount = static_cast<unsigned int>(D.lastSigDigit - D.firstSigDigit) + 1;
2235 partCount = partCountForBits(1 + 196 * partCount / 59);
2236 decSignificand = new integerPart[partCount + 1];
2239 /* Convert to binary efficiently - we do almost all multiplication
2240 in an integerPart. When this would overflow do we do a single
2241 bignum multiplication, and then revert again to multiplication
2242 in an integerPart. */
2244 integerPart decValue, val, multiplier;
2253 decValue = decDigitValue(*p++);
2255 val = val * 10 + decValue;
2256 /* The maximum number that can be multiplied by ten with any
2257 digit added without overflowing an integerPart. */
2258 } while (p <= D.lastSigDigit && multiplier <= (~ (integerPart) 0 - 9) / 10);
2260 /* Multiply out the current part. */
2261 APInt::tcMultiplyPart(decSignificand, decSignificand, multiplier, val,
2262 partCount, partCount + 1, false);
2264 /* If we used another part (likely but not guaranteed), increase
2266 if (decSignificand[partCount])
2268 } while (p <= D.lastSigDigit);
2270 category = fcNormal;
2271 fs = roundSignificandWithExponent(decSignificand, partCount,
2272 D.exponent, rounding_mode);
2274 delete [] decSignificand;
2281 APFloat::convertFromString(const char *p, roundingMode rounding_mode)
2283 assertArithmeticOK(*semantics);
2285 /* Handle a leading minus sign. */
2291 if(p[0] == '0' && (p[1] == 'x' || p[1] == 'X'))
2292 return convertFromHexadecimalString(p + 2, rounding_mode);
2294 return convertFromDecimalString(p, rounding_mode);
2297 /* Write out a hexadecimal representation of the floating point value
2298 to DST, which must be of sufficient size, in the C99 form
2299 [-]0xh.hhhhp[+-]d. Return the number of characters written,
2300 excluding the terminating NUL.
2302 If UPPERCASE, the output is in upper case, otherwise in lower case.
2304 HEXDIGITS digits appear altogether, rounding the value if
2305 necessary. If HEXDIGITS is 0, the minimal precision to display the
2306 number precisely is used instead. If nothing would appear after
2307 the decimal point it is suppressed.
2309 The decimal exponent is always printed and has at least one digit.
2310 Zero values display an exponent of zero. Infinities and NaNs
2311 appear as "infinity" or "nan" respectively.
2313 The above rules are as specified by C99. There is ambiguity about
2314 what the leading hexadecimal digit should be. This implementation
2315 uses whatever is necessary so that the exponent is displayed as
2316 stored. This implies the exponent will fall within the IEEE format
2317 range, and the leading hexadecimal digit will be 0 (for denormals),
2318 1 (normal numbers) or 2 (normal numbers rounded-away-from-zero with
2319 any other digits zero).
2322 APFloat::convertToHexString(char *dst, unsigned int hexDigits,
2323 bool upperCase, roundingMode rounding_mode) const
2327 assertArithmeticOK(*semantics);
2335 memcpy (dst, upperCase ? infinityU: infinityL, sizeof infinityU - 1);
2336 dst += sizeof infinityL - 1;
2340 memcpy (dst, upperCase ? NaNU: NaNL, sizeof NaNU - 1);
2341 dst += sizeof NaNU - 1;
2346 *dst++ = upperCase ? 'X': 'x';
2348 if (hexDigits > 1) {
2350 memset (dst, '0', hexDigits - 1);
2351 dst += hexDigits - 1;
2353 *dst++ = upperCase ? 'P': 'p';
2358 dst = convertNormalToHexString (dst, hexDigits, upperCase, rounding_mode);
2364 return static_cast<unsigned int>(dst - p);
2367 /* Does the hard work of outputting the correctly rounded hexadecimal
2368 form of a normal floating point number with the specified number of
2369 hexadecimal digits. If HEXDIGITS is zero the minimum number of
2370 digits necessary to print the value precisely is output. */
2372 APFloat::convertNormalToHexString(char *dst, unsigned int hexDigits,
2374 roundingMode rounding_mode) const
2376 unsigned int count, valueBits, shift, partsCount, outputDigits;
2377 const char *hexDigitChars;
2378 const integerPart *significand;
2383 *dst++ = upperCase ? 'X': 'x';
2386 hexDigitChars = upperCase ? hexDigitsUpper: hexDigitsLower;
2388 significand = significandParts();
2389 partsCount = partCount();
2391 /* +3 because the first digit only uses the single integer bit, so
2392 we have 3 virtual zero most-significant-bits. */
2393 valueBits = semantics->precision + 3;
2394 shift = integerPartWidth - valueBits % integerPartWidth;
2396 /* The natural number of digits required ignoring trailing
2397 insignificant zeroes. */
2398 outputDigits = (valueBits - significandLSB () + 3) / 4;
2400 /* hexDigits of zero means use the required number for the
2401 precision. Otherwise, see if we are truncating. If we are,
2402 find out if we need to round away from zero. */
2404 if (hexDigits < outputDigits) {
2405 /* We are dropping non-zero bits, so need to check how to round.
2406 "bits" is the number of dropped bits. */
2408 lostFraction fraction;
2410 bits = valueBits - hexDigits * 4;
2411 fraction = lostFractionThroughTruncation (significand, partsCount, bits);
2412 roundUp = roundAwayFromZero(rounding_mode, fraction, bits);
2414 outputDigits = hexDigits;
2417 /* Write the digits consecutively, and start writing in the location
2418 of the hexadecimal point. We move the most significant digit
2419 left and add the hexadecimal point later. */
2422 count = (valueBits + integerPartWidth - 1) / integerPartWidth;
2424 while (outputDigits && count) {
2427 /* Put the most significant integerPartWidth bits in "part". */
2428 if (--count == partsCount)
2429 part = 0; /* An imaginary higher zero part. */
2431 part = significand[count] << shift;
2434 part |= significand[count - 1] >> (integerPartWidth - shift);
2436 /* Convert as much of "part" to hexdigits as we can. */
2437 unsigned int curDigits = integerPartWidth / 4;
2439 if (curDigits > outputDigits)
2440 curDigits = outputDigits;
2441 dst += partAsHex (dst, part, curDigits, hexDigitChars);
2442 outputDigits -= curDigits;
2448 /* Note that hexDigitChars has a trailing '0'. */
2451 *q = hexDigitChars[hexDigitValue (*q) + 1];
2452 } while (*q == '0');
2455 /* Add trailing zeroes. */
2456 memset (dst, '0', outputDigits);
2457 dst += outputDigits;
2460 /* Move the most significant digit to before the point, and if there
2461 is something after the decimal point add it. This must come
2462 after rounding above. */
2469 /* Finally output the exponent. */
2470 *dst++ = upperCase ? 'P': 'p';
2472 return writeSignedDecimal (dst, exponent);
2475 // For good performance it is desirable for different APFloats
2476 // to produce different integers.
2478 APFloat::getHashValue() const
2480 if (category==fcZero) return sign<<8 | semantics->precision ;
2481 else if (category==fcInfinity) return sign<<9 | semantics->precision;
2482 else if (category==fcNaN) return 1<<10 | semantics->precision;
2484 uint32_t hash = sign<<11 | semantics->precision | exponent<<12;
2485 const integerPart* p = significandParts();
2486 for (int i=partCount(); i>0; i--, p++)
2487 hash ^= ((uint32_t)*p) ^ (uint32_t)((*p)>>32);
2492 // Conversion from APFloat to/from host float/double. It may eventually be
2493 // possible to eliminate these and have everybody deal with APFloats, but that
2494 // will take a while. This approach will not easily extend to long double.
2495 // Current implementation requires integerPartWidth==64, which is correct at
2496 // the moment but could be made more general.
2498 // Denormals have exponent minExponent in APFloat, but minExponent-1 in
2499 // the actual IEEE respresentations. We compensate for that here.
2502 APFloat::convertF80LongDoubleAPFloatToAPInt() const
2504 assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended);
2505 assert (partCount()==2);
2507 uint64_t myexponent, mysignificand;
2509 if (category==fcNormal) {
2510 myexponent = exponent+16383; //bias
2511 mysignificand = significandParts()[0];
2512 if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL))
2513 myexponent = 0; // denormal
2514 } else if (category==fcZero) {
2517 } else if (category==fcInfinity) {
2518 myexponent = 0x7fff;
2519 mysignificand = 0x8000000000000000ULL;
2521 assert(category == fcNaN && "Unknown category");
2522 myexponent = 0x7fff;
2523 mysignificand = significandParts()[0];
2527 words[0] = ((uint64_t)(sign & 1) << 63) |
2528 ((myexponent & 0x7fffLL) << 48) |
2529 ((mysignificand >>16) & 0xffffffffffffLL);
2530 words[1] = mysignificand & 0xffff;
2531 return APInt(80, 2, words);
2535 APFloat::convertPPCDoubleDoubleAPFloatToAPInt() const
2537 assert(semantics == (const llvm::fltSemantics*)&PPCDoubleDouble);
2538 assert (partCount()==2);
2540 uint64_t myexponent, mysignificand, myexponent2, mysignificand2;
2542 if (category==fcNormal) {
2543 myexponent = exponent + 1023; //bias
2544 myexponent2 = exponent2 + 1023;
2545 mysignificand = significandParts()[0];
2546 mysignificand2 = significandParts()[1];
2547 if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
2548 myexponent = 0; // denormal
2549 if (myexponent2==1 && !(mysignificand2 & 0x10000000000000LL))
2550 myexponent2 = 0; // denormal
2551 } else if (category==fcZero) {
2556 } else if (category==fcInfinity) {
2562 assert(category == fcNaN && "Unknown category");
2564 mysignificand = significandParts()[0];
2565 myexponent2 = exponent2;
2566 mysignificand2 = significandParts()[1];
2570 words[0] = ((uint64_t)(sign & 1) << 63) |
2571 ((myexponent & 0x7ff) << 52) |
2572 (mysignificand & 0xfffffffffffffLL);
2573 words[1] = ((uint64_t)(sign2 & 1) << 63) |
2574 ((myexponent2 & 0x7ff) << 52) |
2575 (mysignificand2 & 0xfffffffffffffLL);
2576 return APInt(128, 2, words);
2580 APFloat::convertDoubleAPFloatToAPInt() const
2582 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
2583 assert (partCount()==1);
2585 uint64_t myexponent, mysignificand;
2587 if (category==fcNormal) {
2588 myexponent = exponent+1023; //bias
2589 mysignificand = *significandParts();
2590 if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
2591 myexponent = 0; // denormal
2592 } else if (category==fcZero) {
2595 } else if (category==fcInfinity) {
2599 assert(category == fcNaN && "Unknown category!");
2601 mysignificand = *significandParts();
2604 return APInt(64, ((((uint64_t)(sign & 1) << 63) |
2605 ((myexponent & 0x7ff) << 52) |
2606 (mysignificand & 0xfffffffffffffLL))));
2610 APFloat::convertFloatAPFloatToAPInt() const
2612 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
2613 assert (partCount()==1);
2615 uint32_t myexponent, mysignificand;
2617 if (category==fcNormal) {
2618 myexponent = exponent+127; //bias
2619 mysignificand = (uint32_t)*significandParts();
2620 if (myexponent == 1 && !(mysignificand & 0x800000))
2621 myexponent = 0; // denormal
2622 } else if (category==fcZero) {
2625 } else if (category==fcInfinity) {
2629 assert(category == fcNaN && "Unknown category!");
2631 mysignificand = (uint32_t)*significandParts();
2634 return APInt(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
2635 (mysignificand & 0x7fffff)));
2638 // This function creates an APInt that is just a bit map of the floating
2639 // point constant as it would appear in memory. It is not a conversion,
2640 // and treating the result as a normal integer is unlikely to be useful.
2643 APFloat::bitcastToAPInt() const
2645 if (semantics == (const llvm::fltSemantics*)&IEEEsingle)
2646 return convertFloatAPFloatToAPInt();
2648 if (semantics == (const llvm::fltSemantics*)&IEEEdouble)
2649 return convertDoubleAPFloatToAPInt();
2651 if (semantics == (const llvm::fltSemantics*)&PPCDoubleDouble)
2652 return convertPPCDoubleDoubleAPFloatToAPInt();
2654 assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended &&
2656 return convertF80LongDoubleAPFloatToAPInt();
2660 APFloat::convertToFloat() const
2662 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
2663 APInt api = bitcastToAPInt();
2664 return api.bitsToFloat();
2668 APFloat::convertToDouble() const
2670 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
2671 APInt api = bitcastToAPInt();
2672 return api.bitsToDouble();
2675 /// Integer bit is explicit in this format. Intel hardware (387 and later)
2676 /// does not support these bit patterns:
2677 /// exponent = all 1's, integer bit 0, significand 0 ("pseudoinfinity")
2678 /// exponent = all 1's, integer bit 0, significand nonzero ("pseudoNaN")
2679 /// exponent = 0, integer bit 1 ("pseudodenormal")
2680 /// exponent!=0 nor all 1's, integer bit 0 ("unnormal")
2681 /// At the moment, the first two are treated as NaNs, the second two as Normal.
2683 APFloat::initFromF80LongDoubleAPInt(const APInt &api)
2685 assert(api.getBitWidth()==80);
2686 uint64_t i1 = api.getRawData()[0];
2687 uint64_t i2 = api.getRawData()[1];
2688 uint64_t myexponent = (i1 >> 48) & 0x7fff;
2689 uint64_t mysignificand = ((i1 << 16) & 0xffffffffffff0000ULL) |
2692 initialize(&APFloat::x87DoubleExtended);
2693 assert(partCount()==2);
2695 sign = static_cast<unsigned int>(i1>>63);
2696 if (myexponent==0 && mysignificand==0) {
2697 // exponent, significand meaningless
2699 } else if (myexponent==0x7fff && mysignificand==0x8000000000000000ULL) {
2700 // exponent, significand meaningless
2701 category = fcInfinity;
2702 } else if (myexponent==0x7fff && mysignificand!=0x8000000000000000ULL) {
2703 // exponent meaningless
2705 significandParts()[0] = mysignificand;
2706 significandParts()[1] = 0;
2708 category = fcNormal;
2709 exponent = myexponent - 16383;
2710 significandParts()[0] = mysignificand;
2711 significandParts()[1] = 0;
2712 if (myexponent==0) // denormal
2718 APFloat::initFromPPCDoubleDoubleAPInt(const APInt &api)
2720 assert(api.getBitWidth()==128);
2721 uint64_t i1 = api.getRawData()[0];
2722 uint64_t i2 = api.getRawData()[1];
2723 uint64_t myexponent = (i1 >> 52) & 0x7ff;
2724 uint64_t mysignificand = i1 & 0xfffffffffffffLL;
2725 uint64_t myexponent2 = (i2 >> 52) & 0x7ff;
2726 uint64_t mysignificand2 = i2 & 0xfffffffffffffLL;
2728 initialize(&APFloat::PPCDoubleDouble);
2729 assert(partCount()==2);
2731 sign = static_cast<unsigned int>(i1>>63);
2732 sign2 = static_cast<unsigned int>(i2>>63);
2733 if (myexponent==0 && mysignificand==0) {
2734 // exponent, significand meaningless
2735 // exponent2 and significand2 are required to be 0; we don't check
2737 } else if (myexponent==0x7ff && mysignificand==0) {
2738 // exponent, significand meaningless
2739 // exponent2 and significand2 are required to be 0; we don't check
2740 category = fcInfinity;
2741 } else if (myexponent==0x7ff && mysignificand!=0) {
2742 // exponent meaningless. So is the whole second word, but keep it
2745 exponent2 = myexponent2;
2746 significandParts()[0] = mysignificand;
2747 significandParts()[1] = mysignificand2;
2749 category = fcNormal;
2750 // Note there is no category2; the second word is treated as if it is
2751 // fcNormal, although it might be something else considered by itself.
2752 exponent = myexponent - 1023;
2753 exponent2 = myexponent2 - 1023;
2754 significandParts()[0] = mysignificand;
2755 significandParts()[1] = mysignificand2;
2756 if (myexponent==0) // denormal
2759 significandParts()[0] |= 0x10000000000000LL; // integer bit
2763 significandParts()[1] |= 0x10000000000000LL; // integer bit
2768 APFloat::initFromDoubleAPInt(const APInt &api)
2770 assert(api.getBitWidth()==64);
2771 uint64_t i = *api.getRawData();
2772 uint64_t myexponent = (i >> 52) & 0x7ff;
2773 uint64_t mysignificand = i & 0xfffffffffffffLL;
2775 initialize(&APFloat::IEEEdouble);
2776 assert(partCount()==1);
2778 sign = static_cast<unsigned int>(i>>63);
2779 if (myexponent==0 && mysignificand==0) {
2780 // exponent, significand meaningless
2782 } else if (myexponent==0x7ff && mysignificand==0) {
2783 // exponent, significand meaningless
2784 category = fcInfinity;
2785 } else if (myexponent==0x7ff && mysignificand!=0) {
2786 // exponent meaningless
2788 *significandParts() = mysignificand;
2790 category = fcNormal;
2791 exponent = myexponent - 1023;
2792 *significandParts() = mysignificand;
2793 if (myexponent==0) // denormal
2796 *significandParts() |= 0x10000000000000LL; // integer bit
2801 APFloat::initFromFloatAPInt(const APInt & api)
2803 assert(api.getBitWidth()==32);
2804 uint32_t i = (uint32_t)*api.getRawData();
2805 uint32_t myexponent = (i >> 23) & 0xff;
2806 uint32_t mysignificand = i & 0x7fffff;
2808 initialize(&APFloat::IEEEsingle);
2809 assert(partCount()==1);
2812 if (myexponent==0 && mysignificand==0) {
2813 // exponent, significand meaningless
2815 } else if (myexponent==0xff && mysignificand==0) {
2816 // exponent, significand meaningless
2817 category = fcInfinity;
2818 } else if (myexponent==0xff && mysignificand!=0) {
2819 // sign, exponent, significand meaningless
2821 *significandParts() = mysignificand;
2823 category = fcNormal;
2824 exponent = myexponent - 127; //bias
2825 *significandParts() = mysignificand;
2826 if (myexponent==0) // denormal
2829 *significandParts() |= 0x800000; // integer bit
2833 /// Treat api as containing the bits of a floating point number. Currently
2834 /// we infer the floating point type from the size of the APInt. The
2835 /// isIEEE argument distinguishes between PPC128 and IEEE128 (not meaningful
2836 /// when the size is anything else).
2838 APFloat::initFromAPInt(const APInt& api, bool isIEEE)
2840 if (api.getBitWidth() == 32)
2841 return initFromFloatAPInt(api);
2842 else if (api.getBitWidth()==64)
2843 return initFromDoubleAPInt(api);
2844 else if (api.getBitWidth()==80)
2845 return initFromF80LongDoubleAPInt(api);
2846 else if (api.getBitWidth()==128 && !isIEEE)
2847 return initFromPPCDoubleDoubleAPInt(api);
2852 APFloat::APFloat(const APInt& api, bool isIEEE)
2854 initFromAPInt(api, isIEEE);
2857 APFloat::APFloat(float f)
2859 APInt api = APInt(32, 0);
2860 initFromAPInt(api.floatToBits(f));
2863 APFloat::APFloat(double d)
2865 APInt api = APInt(64, 0);
2866 initFromAPInt(api.doubleToBits(d));